Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def funk(n):
    k = int((2*n)**0.5)
    for j in range(1,k):
        num1 = ((j)*(j+1))//2
        tmp = n-num1
        d = (1+(8*tmp))
        if d<0:continue

        poss = ((d**0.5)-1)/2
        if poss.is_integer():
            return "YES"
    return "NO"

if __name__ == '__main__':
    n = int(input())
    print(funk(n))